Firstly, I am sorry you find yourself in this situation. I was there too.
Its a long road to travel and you will need Patience. Lots and lots of patience.
I felt the same feelings that you are going through now. They hurt like hell and sometimes it seems that it will never end...Trust me, things will get better. It just takes time.
Keep doing the positive things for yourself and make yourself a better man. But do this for yourself! Not for your wife and not somebody else.
Keep being strong for your kids.
If your wife says she is done... believe her. Give her space and time. She will have to choose to come back if SHE wants to. Start becoming, as they say, the man she would be a fool to leave. Start doing all the DB techniques.
Learn all you can about WAS/LBS etc. Follow Sandi's 37 rules. It will help you understand what she is going through and what you have to go through as well.
There is no guarantee that she will come back but, don't give her any excuses to NOT come back either.
Regarding dating: Proceed cautiously. There is nothing wrong with having a female friend to hang with and talk to but, emotionally you are still probably a wreck from the sounds of your post.
Remember: NO EXPECTATIONS!!!
Keep improving yourself and taking care of your kids. You don't have to give up on your relationship but you cant force anything on it either. Love has to be given freely by both people. Give her time and space and LOTS of it.
I stood for my marriage right up until the papers were signed. That was my line in the sand. I gave our marriage every chance I could to be saved but, it was not enough. And sometimes that is the way it goes. Did I do everything perfect? NO! But I did the best I could. And now I am content with the fact that I tried my best but my best wasn't good enough. It was certainly not what I wanted but, when my wife said she was done, she was done. Results will vary.
Advice is free and normally I charge .02 cents for mine but today it is free Learn as much as you can about what you and your wife are going through. Then, try to do everything you can to give your marriage the best chance of survival. When the dust settles, regardless of how it goes, you can sleep at night with no regrets.
That is where I find myself today. I can sleep at night knowing I did the best I could.